By MARK LANDLER

August 11, 2014

For the 19 months since Hillary Rodham Clinton departed as President Obama’s secretary of state, she and Mr. Obama, and their staffs, have labored to preserve a veneer of unity over how they worked together and how they view the world.

On Sunday, the veneer shattered — the victim of Mrs. Clinton’s remarkably blunt interview with Jeffrey Goldberg, a writer for The Atlantic, in which she criticized not just Mr. Obama’s refusal to aid the rebels in Syria, but his shorthand description of his entire foreign policy.

“Great nations need organizing principles, and ‘Don’t do stupid stuff’ is not an organizing principle,” Mrs. Clinton said, referring to the line that Mr. Obama has used with aides and reporters to describe his reluctance to inject the United States into messy foreign conflicts.

Mrs. Clinton said she assumed the line was more a “political message” for a war-weary American public than his worldview — an interpretation that makes her words even more stinging, since “Don’t do stupid stuff” was in fact the animating principle for the foreign-policy blueprint that Mr. Obama laid out in a speech at West Point in May.

That Mrs. Clinton is more hawkish than Mr. Obama is no surprise to anyone who watched a Democratic primary debate in 2008. Her policy differences with the president during his first term were well documented, though they were less about underlying strategy than tactics.

She favored supplying arms to moderate Syrian rebels, leaving behind a somewhat larger residual military force in Iraq and waiting longer before withdrawing American support for President Hosni Mubarak of Egypt during the historic protests in Cairo.

What has changed is her readiness to raise those differences to the surface and put them in the context of a different worldview. Even her memoir “Hard Choices,” which she was promoting in her interview with Mr. Goldberg, soft-pedaled the gaps and painted a portrait of her and Mr. Obama in lock step in rebuilding America’s tattered image abroad.

Now, though, Mrs. Clinton is suggesting that she and the president hold different views on how best to project American power: His view is cautious, inward-looking, suffused with a sense of limits, while hers is muscular, optimistic, unabashedly old-fashioned.

“You know, when you’re down on yourself, and when you are hunkering down and pulling back, you’re not going to make any better decisions than when you were aggressively, belligerently putting yourself forward,” Mrs. Clinton said to Mr. Goldberg. “One issue is that we don’t even tell our own story very well these days.”

Much of the interview’s resonance is in its timing, coming two days after Mr. Obama authorized airstrikes against Sunni militants in Iraq. Mrs. Clinton’s aides say this was an unfortunate coincidence; the session was scheduled before anyone knew about military action, which has “amplified a statement about militants” she has made before.

Still, when Mrs. Clinton says that “the failure to help build up a credible fighting force” against President Bashar al-Assad in Syria “left a big vacuum, which the jihadists have now filled,” the suggestion is that Mr. Obama’s refusal to arm the rebels might end up being a singular misjudgment. But at the time of the Obama administration’s internal debate over that decision, several officials said, Mrs. Clinton’s advocacy was far less thunderous: The United States had tried every diplomatic gambit with Syria, she said, and nothing else had worked, so why not try funneling weapons to the moderate rebels.

As Mrs. Clinton stakes out her own foreign policy positions in advance of a possible campaign for the White House, it is only natural that some of her statements will not be entirely in sync with her record as secretary of state, when she served at the pleasure of the president.

At the end of her tenure, for example, Mrs. Clinton wrote a memo to Mr. Obama recommending that the United States lift its half-century-old trade embargo against Cuba. It was not a position that she seriously advocated while at the State Department, officials said.

In the interview with The Atlantic, Mrs. Clinton said she had always been in the camp of those who believed that Iran had no right to enrich uranium. Yet in December 2010, she was one of the first American officials to acknowledge publicly, in an interview with the BBC, that Iran could emerge from a nuclear deal with the right to enrich.

Mrs. Clinton also lined up solidly with Prime Minister Benjamin Netanyahu of Israel — a starkly different position from the first term, when she often had to play the heavy during peace negotiations, chiding Mr. Netanyahu for refusing to curb settlement construction.

Even on the Gaza conflict, about which the State Department harshly criticized Israel recently for the number of civilian deaths, she said, “I’m not sure it’s possible to parcel out blame” because of the “fog of war.”

Mrs. Clinton is not the only former cabinet member to part company with Mr. Obama on foreign policy. Robert M. Gates, the former defense secretary, wrote a memoir laced with criticism of the administration’s approach to Afghanistan and other crises.

In an interview with The New York Times in April, Leon E. Panetta, the former defense secretary and C.I.A. director, said of Mr. Obama, “The concern is, the president defining what America’s role in the world is in the 21st century hasn’t happened.”

But Mrs. Clinton is not just any former cabinet member. Because of their long history and Mrs. Clinton’s political future, advisers to her and Mr. Obama have worked especially hard to head off any discord. Her staff gave parts of her memoir to Benjamin J. Rhodes, a deputy national security adviser, for review before publication.

Their interlocking staffs have furthered that effort. Jake Sullivan, Mrs. Clinton’s top policy aide at the State Department, went to work as national security adviser to Vice President Joseph R. Biden Jr., a post that allowed him to convey the White House’s sensitivities to her aides.

Mrs. Clinton hired Tommy Vietor, a longtime Obama aide who was the spokesman for the National Security Council, to help with the rollout of her book. Mrs. Clinton’s aides worried that some in the news media might use the book to try to drive a wedge between her and the president; Mr. Vietor’s job was to push back on that effort.

During the Crimea crisis, the White House chief of staff, Denis McDonough, invited in Clinton aides, including Philippe Reines and Huma Abedin, for consultations. Mrs. Clinton also checks in by email with Mr. Rhodes on issues like Myanmar, in which both have a special interest. And she lunches periodically with Mr. Obama.

How well those ties will weather Mrs. Clinton’s latest remarks remains to be seen.